Metadata Dependent Mondrian Processes

Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1339-1347, 2015.

Abstract

Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure.

Related Material

@InProceedings{pmlr-v37-wangd15,
title = {Metadata Dependent Mondrian Processes},
author = {Yi Wang and Bin Li and Yang Wang and Fang Chen},
booktitle = {Proceedings of the 32nd International Conference on Machine Learning},
pages = {1339--1347},
year = {2015},
editor = {Francis Bach and David Blei},
volume = {37},
series = {Proceedings of Machine Learning Research},
address = {Lille, France},
month = {07--09 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v37/wangd15.pdf},
url = {http://proceedings.mlr.press/v37/wangd15.html},
abstract = {Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure.}
}

%0 Conference Paper
%T Metadata Dependent Mondrian Processes
%A Yi Wang
%A Bin Li
%A Yang Wang
%A Fang Chen
%B Proceedings of the 32nd International Conference on Machine Learning
%C Proceedings of Machine Learning Research
%D 2015
%E Francis Bach
%E David Blei
%F pmlr-v37-wangd15
%I PMLR
%J Proceedings of Machine Learning Research
%P 1339--1347
%U http://proceedings.mlr.press
%V 37
%W PMLR
%X Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure.

TY - CPAPER
TI - Metadata Dependent Mondrian Processes
AU - Yi Wang
AU - Bin Li
AU - Yang Wang
AU - Fang Chen
BT - Proceedings of the 32nd International Conference on Machine Learning
PY - 2015/06/01
DA - 2015/06/01
ED - Francis Bach
ED - David Blei
ID - pmlr-v37-wangd15
PB - PMLR
SP - 1339
DP - PMLR
EP - 1347
L1 - http://proceedings.mlr.press/v37/wangd15.pdf
UR - http://proceedings.mlr.press/v37/wangd15.html
AB - Stochastic partition processes in a product space play an important role in modeling relational data. Recent studies on the Mondrian process have introduced more flexibility into the block structure in relational models. A side-effect of such high flexibility is that, in data sparsity scenarios, the model is prone to overfit. In reality, relational entities are always associated with meta information, such as user profiles in a social network. In this paper, we propose a metadata dependent Mondrian process (MDMP) to incorporate meta information into the stochastic partition process in the product space and the entity allocation process on the resulting block structure. MDMP can not only encourage homogeneous relational interactions within blocks but also discourage meta-label diversity within blocks. Regularized by meta information, MDMP becomes more robust in data sparsity scenarios and easier to converge in posterior inference. We apply MDMP to link prediction and rating prediction and demonstrate that MDMP is more effective than the baseline models in prediction accuracy with a more parsimonious model structure.
ER -